1. Field of the Invention
The present invention relates generally to the design and fabrication of signal processing circuits. More particularly, the present invention relates to the development of a library of operators, along with a system and method for using the operators, to design and fabricate customized integrated circuits which implement digital signal processing in a delta sigma domain.
2. State of the Art
General Signal Processing
Those skilled in the art will appreciate that signal processing can be performed in an analog domain (analog signal processing) or in a sampled domain (digital signal processing). In the analog domain, signals are infinitely variable, while in the digital domain signal variations occur in discrete intervals, both in time and amplitude with the length of the intervals, being a function of the desired granularity.
Although analog signal processing is performed on input signals in their native domain, it is difficult to implement analog circuit components with high precision. That is, analog signal processing circuits involve the use of components which cannot be precisely matched. Further, analog circuits are susceptible to signal drift and to environmental noise. These circuits therefore require substantial overhead (e.g., filtering) to maintain signal integrity. Despite these drawbacks, analog signal processing is still used where, for example, real time processing is required.
For applications where the signal processing delays of digital signal processors can be tolerated, digital signal processing is used because of its non-susceptibility to drift and the influences of environmental noise, and because of its ability to provide high precision results. With conventional multibit digital signal processing, a multibit sample of an analog signal is obtained at each of a plurality of the discrete sampling instances. Each multibit value approximates the level which the analog signal possesses at that time.
One multibit technique for converting an analog signal into a sampled signal is known in the art as pulse code modulation (PCM). Here, a multibit binary number is used to represent the magnitude of the analog signal at each sampled interval. However, high resolution PCM digital signal processing can only be achieved with high circuit complexity and with relatively slow sequential digital processing.
Digital signal processing (DSP) systems such as PCM systems typically operate on an analog signal by using an analog-to-digital converter to produce the multibit values as an approximation of the analog signal. That is, the multibit levels constitute an approximation of magnitudes of the analog signal at discrete points in time. Any differences between the original analog signal and the sampled signal can be considered quantization noise which has been added to the signal (that is, quantization error).
PCM processing is performed by taking Nyquist sampling into account (i.e., sampling is performed at a minimum of twice the highest frequency of the analog signal) to ensure that the original analog signal can be reconstructed. When sampling at the Nyquist frequency, the quantization noise can only occupy space in the frequency domain at which the original signal exists. In the frequency domain, noise from the quantizer spreads from DC to one-half of the Nyquist rate as described, for example, in a document entitled xe2x80x9cPrinciples of Sigma-Delta Modulation for Analog-to-Digital Convertersxe2x80x9d available from Motorola, Inc. (see, for example, page 8). However, because the band, within which the quantization noise is spread, corresponds to the band from which the original analog signal is to be retrieved, it is difficult to distinguish and retrieve the original signal. Because the number of levels of the analog-to-digital converter is proportional to the precision or accuracy with which the signal can be represented, such converters tend to be complex and expensive. Further, conventional digital signal processors may be inappropriate for real time applications since they are based on relatively slow sequential signal processing and the use of a centralized digital signal processor.
More recently, a delta sigma (also referred to as a xe2x80x9csigma deltaxe2x80x9d) approach has been used to implement analog-to-digital conversion. With a typical delta sigma converters, rather than going directly to a multilevel representation of an analog signal, an intermediate stage is used to implement oversampling. Such oversampling is performed at a rate much higher than the necessary Nyquist frequency, but with a reduced number of quantization levels.
The oversampling of a delta sigma approach spreads the quantization noise over the band from DC up to one-half of the oversample rate (which is relatively high in comparison to the Nyquist frequency). Because oversampling is performed at a relatively high frequency, the quantization noise is now spread over a band which extends to a limit much higher than the signal band of interest. Therefore, the amount of noise in the signal band of interest is reduced. Such a configuration permits a (digital) filter to easily separate the signal of interest, and is widely used for high resolution analog-to-digital converters. Conventional analog-to-digital converters typically include a digital decimation filter that subsequently passes the signal band and rejects the noise, thereby providing a multibit word output at the Nyquist rate (i.e., a rate sufficient to fully represent the analog signal).
A similar reverse technique can be used to provide digital-to-analog conversion. After further processing with multibit digital signal processing components, the output from the digital signal processor can be converted back to an analog signal by using a filter to interpolate between the Nyquist samples. The resultant signal which is now smooth is resampled at a much higher rate, adding quantization noise to produce a bit stream. This bit stream is then supplied to a continuous time analog filter to reconstruct the original analog signal.
The reduction of noise in the signal band of interest can be more significantly reduced by including the quantizer in a closed loop. A filter can be included in the loop to shape the quantization noise. If the forward gain of the path has high DC gain, it suppresses the quantization noise at the lower frequencies.
Having explained noise shaping with respect to a first order modulator wherein noise rises proportional to frequency, it will be appreciated that different order modulators can be used to adjust the noise shape. Higher order filters decrease the portion of the quantization noise present in a signal band of interest.
For example, with a second order modulator, for every doubling of the oversample ratio (the ratio of the oversample rate to the Nyquist frequency), 2.5 bits of enhanced resolution can be achieved. Thus, even if a single threshold quantizer which only gives a one bit result is used, oversampling at 1000 times greater than the Nyquist rate results in ten doublings and produces 25 bits of available resolution. The residual noise in the signal band would be represented by only one of the 25 bits or one part in 32 million. A document entitled xe2x80x9cAn Overview of Sigma-Delta-Convertersxe2x80x9d by Pervez M. Aziz et al (IEEE Signal Processing Magazine, January 1996), page 82, compares different resolutions achieved with different delta sigma modulators.
In sum, delta sigma modulation has been used as an intermediate step to producing multibit (PCM) digital signal processing, wherein the quantization noise of a bit stream is spread across a frequency band greater than the signal band of interest. However, because the delta sigma modulation is merely used as an intermediate step to multibit processing, the signal processing delays and the circuit complexities which result when changing from the filtering word lengths in the multibit domain are incurred.
Delta Sigma Processing
More recently, it has been realized that delta sigma signals can be processed in the bit stream domain, without conversion to a multibit (e.g., PCM) signal. Such processing is possible because the density of ones or zeros at any given point in the bit stream represents the analog information to be conveyed. Thus, a single wire can be used to convey all of the analog signal information.
For example, a document entitled xe2x80x9cSigma-Delta Signal Processingxe2x80x9d by Victor de Fonte Dias, IEEE International Symposium on Circuits and Systems, Volume 5, 1994, pages 421-424 describes the conceptual use of operators for processing analog signals as bit streams in the delta sigma domain. One operator described in the Dias document is an adder for summing two bit streams in the delta sigma domain. Afterwards, the resultant signal is supplied to a remodulator to maintain the output in the delta sigma domain. Thus, this document reflects recognition that operations such as addition can be performed on the bit stream in the delta sigma domain.
However, one drawback of the adder described in the Dias document is that it is not a general purpose operator. That is, if the two inputs exceed one half of the available range of possible input signal values, the remodulator will saturate. Further, there is no description of a generalized approach to providing operators for processing signals in the delta sigma domain in a manner which scales inputs to ensure that valid, bounded intermediate processing results will be obtained. Because no such generalized approach is disclosed, the operators cannot be randomly chained together to implement complex processing functions in the delta sigma domain.
Another example of signal processing in the delta sigma domain is described in a document entitled xe2x80x9cRealization and Implementation of a Sigma-Delta Bitstream FIR Filterxe2x80x9d by Simon Kershaw et at, dated 12/1995, pages 1-27, wherein single-input signal processing for filtering signals is disclosed. This document indicates that the overhead associated with analog-to-digital conversion, and with the digital-to-analog conversion in conventional multibit digital signal processors is relatively high. The Kershaw document therefore describes operating in the delta sigma domain to reduce this overhead. However, the Kershaw document only operates on a single input signal, and permits multibit values to occur during the intermediate signal processing. Conversion back to the delta sigma domain occurs only after all of the lumped PCM processing has been completed. That is, a lumped multibit-PCM processor is included in the circuit, such that generalized operators which operate on multiple inputs and which function entirely within the delta sigma domain are not disclosed. Consequently, drawbacks similar to those associated with the conventional use of delta sigma processing as an intermediate step to multibit processing are incurred (e.g., increased circuit complexity as word lengths grow in the multibit processing portion of the circuit).
Another Kershaw et at document entitled xe2x80x9cDigital Signal Processing on a Sigma-Delta Bitstreamxe2x80x9d (undated) also describes signal processing of a single input in the delta sigma domain. However, like the aforementioned Kershaw et at document, this Kershaw et at document fails to describe a generalized approach which is amenable to simplified circuit design and fabrication for processing multiple inputs in the delta sigma domain.
Recognizing that multibit digital processing is unsuitable for all applications (such as real time applications), and recognizing the drawbacks of analog signal processing (e.g., susceptibility to drift, noise and the difficulty in matching components), it would be desirable to design and fabricate circuits in the delta sigma domain. However, at present, there is no generalized system or method available for accommodating the design and fabrication of circuits in the delta sigma domain in a manner which ensures that valid results are obtained from each phase of signal processing, and in a manner which ensures that intermediate results are maintained in the delta sigma domain.
The present invention is directed to providing a generalized system and method for enabling circuit design and fabrication in the delta sigma domain. In accordance with exemplary embodiments, a framework for such a system is based on a library of generalized operators that can receive multiple inputs, and that can be randomly chained together. Further, the operators are specifically configured to guarantee valid (e.g., bounded and/or stable) results, and to provide closure within the delta sigma domain; that is, to produce valid intermediate results in the delta sigma domain. Linear operators are configured to provide closure by complying with at least two criteria: (1) with respect to linear operators, at least one of (a) the inputs and (b) the output of a portion of the operator used to implement a mathematical function is scaled (e.g., normalized) to guarantee valid results; and (2) outputs from each mathematical operation are remodulated into a single bit stream in the delta sigma domain. Further, nonlinear operators such as multiplication operators, are configured with an eye toward producing valid results in the delta sigma domain. For example, with respect to nonlinear operators such as multipliers, at least one operand is restricted to being a non-delta sigma input (i.e., quantization noise-free). As with linear operators, the outputs from portions of nonlinear operators used to implement mathematical operations are remodulated to a single bit stream in the delta sigma domain.
Having established a generalized library of operators as a framework, exemplary embodiments of the present invention are further directed to a system and method for using the library to design and fabricate circuits in the delta sigma domain. Exemplary embodiments exploit the availability of existing design and fabrication tools to initially capture a behavioral model of an analog circuit using ideal analog operators. In accordance with exemplary embodiments of the present invention, these ideal analog operators are used to generate an xe2x80x9canalogxe2x80x9d netlist which is then translated into a xe2x80x9clogicxe2x80x9d netlist using the generalized library of delta sigma operators. For this purpose, the delta sigma operators are configured to correspond one for one with the ideal analog operators. Once the analog operators have been translated into logic using the delta sigma operators, the logic circuit design can be routed and fabricated using available routing and fabrication tools.
Exemplary embodiments of the present invention provide significant advantages. For example, because a generalized library of delta sigma operators is used, the operators can be randomly chained together to implement any analog circuit which has been configured using the analog capture tool. Thus, the benefits of processing input signals in the analog domain can be preserved (e.g., high speed processing for real time applications), along with the benefits of digital signal processing (e.g., immunity to drift and noise). Further, the overall design process can be significantly simplified, since a block analog diagram, which is readily familiar to the circuit designer, can be directly translated into a set of operators in the delta sigma domain. Because exemplary embodiments can use existing circuit design and fabrication tools, the circuit designer needs no special understanding of delta sigma processing. Rather, a behavioral model of a circuit can be designed and simulated in the analog domain, and then be automatically translated into the delta sigma domain for fast, cost-effective implementation as a logic array in any target logic device (e.g., field programmable gate array, application specific integrated circuit and so forth).